On spectral synthesis for sets of the form ๐ธ=\overline{๐๐๐ก(๐ธ)}
On spectral synthesis for sets of the form ๐ธ=\overline{๐๐๐ก(๐ธ)}
The existence of a Helson set disobeying spectral synthesis is combined with the modified Herz criterion to construct a subset <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E"> <mml:semantics> <mml:mi>E</mml:mi> <mml:annotation encoding="application/x-tex">E</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of the circle such that spectral synthesis holds for <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E"> <mml:semantics> <mml:mi>E</mml:mi> โฆ